{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VNXKGEFDBZ6MJRFWZMSUKOKK6Q","short_pith_number":"pith:VNXKGEFD","canonical_record":{"source":{"id":"1202.4625","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T12:45:24Z","cross_cats_sorted":[],"title_canon_sha256":"cf40553d73dbff32327efbb8caf1a837bf1b73e9bf1e0925bdf8d783509ca142","abstract_canon_sha256":"e839f8512a56cced97fae15b97c702769f3d0065802f6b547e0bbbe5e18a530b"},"schema_version":"1.0"},"canonical_sha256":"ab6ea310a30e7cc4c4b6cb2545394af41d3515a29cbdb9b3c13f25e350d8224c","source":{"kind":"arxiv","id":"1202.4625","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4625","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4625v1","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4625","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"VNXKGEFDBZ6M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VNXKGEFDBZ6MJRFW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VNXKGEFD","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VNXKGEFDBZ6MJRFWZMSUKOKK6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4625","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T12:45:24Z","cross_cats_sorted":[],"title_canon_sha256":"cf40553d73dbff32327efbb8caf1a837bf1b73e9bf1e0925bdf8d783509ca142","abstract_canon_sha256":"e839f8512a56cced97fae15b97c702769f3d0065802f6b547e0bbbe5e18a530b"},"schema_version":"1.0"},"canonical_sha256":"ab6ea310a30e7cc4c4b6cb2545394af41d3515a29cbdb9b3c13f25e350d8224c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:50.238023Z","signature_b64":"EpQxdT4tPy4jqOOqn7ejEKuQE2sQqCEoacaKtnpb7FT0isf4mkwxmBlJs1KnujoTKjFctqy/Y0Zbgkq3xtvSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab6ea310a30e7cc4c4b6cb2545394af41d3515a29cbdb9b3c13f25e350d8224c","last_reissued_at":"2026-05-18T04:01:50.237349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:50.237349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4625","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XBh0m7ApJLNkX6hpGImCWNEDWJyPtuUvmrtEfp/BPH9eSC4TvyIINAaGWQLodigXG5H9ZaIBVdsIYLzBjadDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:16:55.763613Z"},"content_sha256":"450dc42b4ccb6e4b2fba6b9b39c4aa0e4d8a36bee21f92eab4f6719e98a7fede","schema_version":"1.0","event_id":"sha256:450dc42b4ccb6e4b2fba6b9b39c4aa0e4d8a36bee21f92eab4f6719e98a7fede"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VNXKGEFDBZ6MJRFWZMSUKOKK6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Malliavin calculus for backward stochastic differential equations and application to numerical solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Xiaoming Song, Yaozhong Hu","submitted_at":"2012-02-21T12:45:24Z","abstract_excerpt":"In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the $L^p$-H\\\"{o}lder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic differential equations and obtain the rate of convergence of the schemes based on the obtained $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4625","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KqAFn38AkmsUF0apilZ4ZRFGj9DcoA2xJOS21wKOqImEu/KedgYYoh8TwkX4TS1XCV7QBXvZZVvto/2UfhcKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:16:55.764335Z"},"content_sha256":"4b126730160997117535966832a8b498c6bde310ffdbbc2fb6c66b3a6a4924fa","schema_version":"1.0","event_id":"sha256:4b126730160997117535966832a8b498c6bde310ffdbbc2fb6c66b3a6a4924fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q/bundle.json","state_url":"https://pith.science/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T20:16:55Z","links":{"resolver":"https://pith.science/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q","bundle":"https://pith.science/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q/bundle.json","state":"https://pith.science/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNXKGEFDBZ6MJRFWZMSUKOKK6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VNXKGEFDBZ6MJRFWZMSUKOKK6Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e839f8512a56cced97fae15b97c702769f3d0065802f6b547e0bbbe5e18a530b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T12:45:24Z","title_canon_sha256":"cf40553d73dbff32327efbb8caf1a837bf1b73e9bf1e0925bdf8d783509ca142"},"schema_version":"1.0","source":{"id":"1202.4625","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4625","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4625v1","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4625","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"VNXKGEFDBZ6M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VNXKGEFDBZ6MJRFW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VNXKGEFD","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:4b126730160997117535966832a8b498c6bde310ffdbbc2fb6c66b3a6a4924fa","target":"graph","created_at":"2026-05-18T04:01:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the $L^p$-H\\\"{o}lder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic differential equations and obtain the rate of convergence of the schemes based on the obtained $","authors_text":"David Nualart, Xiaoming Song, Yaozhong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T12:45:24Z","title":"Malliavin calculus for backward stochastic differential equations and application to numerical solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4625","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:450dc42b4ccb6e4b2fba6b9b39c4aa0e4d8a36bee21f92eab4f6719e98a7fede","target":"record","created_at":"2026-05-18T04:01:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e839f8512a56cced97fae15b97c702769f3d0065802f6b547e0bbbe5e18a530b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T12:45:24Z","title_canon_sha256":"cf40553d73dbff32327efbb8caf1a837bf1b73e9bf1e0925bdf8d783509ca142"},"schema_version":"1.0","source":{"id":"1202.4625","kind":"arxiv","version":1}},"canonical_sha256":"ab6ea310a30e7cc4c4b6cb2545394af41d3515a29cbdb9b3c13f25e350d8224c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab6ea310a30e7cc4c4b6cb2545394af41d3515a29cbdb9b3c13f25e350d8224c","first_computed_at":"2026-05-18T04:01:50.237349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:50.237349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EpQxdT4tPy4jqOOqn7ejEKuQE2sQqCEoacaKtnpb7FT0isf4mkwxmBlJs1KnujoTKjFctqy/Y0Zbgkq3xtvSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:50.238023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4625","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:450dc42b4ccb6e4b2fba6b9b39c4aa0e4d8a36bee21f92eab4f6719e98a7fede","sha256:4b126730160997117535966832a8b498c6bde310ffdbbc2fb6c66b3a6a4924fa"],"state_sha256":"b84b57aa853bd9dd94745a0ddb3266ea318126ee5387e6d7e191c309ef1ef2f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bB1wHsT8gF6yH1T2b09BsvK9gKGwYkszyU2xPIym8DesOBzFZClG7Y9AIv7we/L4gDuLy3A5G7iOiEwfXALyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:16:55.767796Z","bundle_sha256":"6df8dfa1257aed8d96965d6d1fec229157f754d8c09492f13eeec2f6066ef255"}}